{
 "metadata": {
  "name": "",
  "signature": "sha256:0a5b63589cb48873e1a288151eb0a1f2a2090300297eaeeb7ff102c9bc218611"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# MTH9879 Homework 1 <font color='blue'> Score: 38/40 </font>\n",
      "\n",
      "<font color='blue'>\n",
      "Please see the corresponding cells for comments (in blue) on each individual question, if there's any.\n",
      "</font>\n",
      "\n",
      "Assigned: February 3, 2015.\n",
      "Due: February 17, 2015 by 6pm. \n",
      "\n",
      "Late homework **will not be accepted**.\n",
      "\n",
      "$$\n",
      "\\newcommand{\\supp}{\\mathrm{supp}}\n",
      "\\newcommand{\\E}{\\mathbb{E} }\n",
      "\\def\\Cov{{ \\mbox{Cov} }}\n",
      "\\def\\Var{{ \\mbox{Var} }}\n",
      "\\newcommand{\\1}{\\mathbf{1} }\n",
      "\\newcommand{\\PP}{\\mathbb{P} }\n",
      "%\\newcommand{\\Pr}{\\mathrm{Pr} }\n",
      "\\newcommand{\\QQ}{\\mathbb{Q} }\n",
      "\\newcommand{\\RR}{\\mathbb{R} }\n",
      "\\newcommand{\\DD}{\\mathbb{D} }\n",
      "\\newcommand{\\HH}{\\mathbb{H} }\n",
      "\\newcommand{\\spn}{\\mathrm{span} }\n",
      "\\newcommand{\\cov}{\\mathrm{cov} }\n",
      "\\newcommand{\\sgn}{\\mathrm{sgn} }\n",
      "\\newcommand{\\HS}{\\mathcal{L}_{\\mathrm{HS}} }\n",
      "%\\newcommand{\\HS}{\\mathrm{HS} }\n",
      "\\newcommand{\\trace}{\\mathrm{trace} }\n",
      "\\newcommand{\\LL}{\\mathcal{L} }\n",
      "%\\newcommand{\\LL}{\\mathrm{L} }\n",
      "\\newcommand{\\s}{\\mathcal{S} }\n",
      "\\newcommand{\\ee}{\\mathcal{E} }\n",
      "\\newcommand{\\ff}{\\mathcal{F} }\n",
      "\\newcommand{\\hh}{\\mathcal{H} }\n",
      "\\newcommand{\\bb}{\\mathcal{B} }\n",
      "\\newcommand{\\dd}{\\mathcal{D} }\n",
      "\\newcommand{\\g}{\\mathcal{G} }\n",
      "\\newcommand{\\p}{\\partial}\n",
      "\\newcommand{\\half}{\\frac{1}{2} }\n",
      "\\newcommand{\\T}{\\mathcal{T} }\n",
      "\\newcommand{\\bi}{\\begin{itemize}}\n",
      "\\newcommand{\\ei}{\\end{itemize}}\n",
      "\\newcommand{\\beq}{\\begin{equation}}\n",
      "\\newcommand{\\eeq}{\\end{equation}}\n",
      "\\newcommand{\\beas}{\\begin{eqnarray*}}\n",
      "\\newcommand{\\eeas}{\\end{eqnarray*}}\n",
      "\\newcommand{\\cO}{\\mathcal{O}}\n",
      "\\newcommand{\\cF}{\\mathcal{F}}\n",
      "\\newcommand{\\cL}{\\mathcal{L}}\n",
      "\\newcommand{\\BS}{\\text{BS}}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### <font color='blue'> Please follow the Homework submission guidline</font>\n",
      "\n",
      "\n",
      "<font color='blue'>\n",
      "http://mfeapp.baruch.cuny.edu/forum/threads/homework-submission-guidelines-spring-2015.10357/. \n",
      "Please rename your iPython notebook as 9879HWx_LastName_FirstName, where x = homework number, and the same for the subject of your email for HW submission. Please include your name in your iPython notebook as the first cell. Any violation gets 20% off from that homework, cumulative.\n",
      "</font>\n",
      "\n",
      "### <font color='blue'> This time will just be a warning. But from HW3 on, \"any violation gets 20% off from that homework, cumulative.\"</font>\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<font color = \"red\">Homework is to be done by each student individually.  To receive full credit, you must email a completed copy of this iPython notebook to Yu Gan (yugan323@gmail.com), Fubo Shi (fubo.shi.baruch@gmail.com), and Tai-Ho Wang (tai-ho.wang@baruch.cuny.edu) by the due date and time.  All R-code must run correctly and solutions must be written up neatly in Markdown/LaTeX format.\n",
      "\n",
      "<font color=\"blue\">If you encounter problems with Markdown/LaTeX or iPython notebook, please contact your TAs Yu Gan and/or Fubo Shi.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 1. (4 points)  <font color='blue'> Score: 4/4 </font>\n",
      "\n",
      "Read Chapter 1 of Market Liquidity by Foucault, Pagano and R&ouml;ell.\n",
      "What algorithmic trading strategy was being used by the seller who triggered the Flash\n",
      "Crash of May 6, 2010? Why did it cause a crash? How could this algorithm have been\n",
      "amended so as to avoid the ensuing disaster?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Solution:\n",
      "\n",
      "Strategy: constant participation rate\n",
      "Reason cause a crash: this strategy is of splitting the order in such a way that each \"child\" order represents a fixed fraction of the total trading volume over a given period of time. The problem is as the parent becomes larger, the sub-orders themselves can gice a false impression of large volume, accelerating the main order's execution, which is a snowball effect.\n",
      "Way to amend it: the trader should make his strategy contingent on the execution price received, trading less as the price impact increases."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Smith Farmer zero-intelligence model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Set up R-environment\n",
      "\n",
      "The following code sources *ziSetup.R* which has all the functions required for the problem."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#%load_ext rmagic\n",
      "%load_ext rpy2.ipython"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "download.file(url=\"http://mfe.baruch.cuny.edu/wp-content/uploads/2015/01/ziSetup.zip\", destfile=\"ziSetup.zip\")\n",
      "unzip(zipfile=\"ziSetup.zip\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "trying URL 'http://mfe.baruch.cuny.edu/wp-content/uploads/2015/01/ziSetup.zip'\n",
        "Content type 'application/zip' length 1485 bytes\n",
        "opened URL\n",
        "==================================================\n",
        "downloaded 1485 bytes\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "source(\"ziSetup.R\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 2. (4 points) <font color='blue'> Score: 4/4 </font>\n",
      "\n",
      "Using the provided functions in *ziSetup.R* (with $\\alpha = 1$, $\\mu = 10$, $\\delta = 1/5$),\n",
      "initialize the order book and add two orders to the (best) bid side of the book. The resulting\n",
      "book should have 3 orders at best bid and 1 order at best offer. Plot the resulting book\n",
      "shape."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R    # Problem 2\n",
      "\n",
      "logging <- F # very important for speed\n",
      "\n",
      "alpha <- 1\n",
      "mu <- 10\n",
      "delta <- 1/5 \n",
      "\n",
      "# Initialize the book\n",
      "initializeBook5()\n",
      "\n",
      "# Add two best bid limit orders into the book \n",
      "limitBuyOrder(bestBid())\n",
      "limitBuyOrder(bestBid())\n",
      "\n",
      "# Start to plot\n",
      "bookPlot(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAYAAAB91L6VAAAEJGlDQ1BJQ0MgUHJvZmlsZQAAOBGF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\nIFCRwP8HdnBj1H4zNt4AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 3. (16 points) <font color='blue'> Score: 16/16 </font>\n",
      "\n",
      "(a) Using the code supplied to generate Figure 2 as a template, simulate 100,000 events, computing the average book shape (in a band $\\pm 20$ around the mid price) for the\n",
      "following sets of parameters:\n",
      "\n",
      "|$\\alpha$|$\\mu$|$\\delta$|\n",
      "-----|-----:|-------:|\n",
      "I| 1 | 10 | $\\frac15$\n",
      "II| 1 | 8 |  $\\frac15$\n",
      "III| 1 |  10 | $\\frac16$\n",
      "IV| 1  | 10 | $\\frac18$ \n",
      "\n",
      "(Warning: This might take longer than 15 minutes to run!).\n",
      "\n",
      "(b) Generate a summary plot of the average book shapes for each parameter set (I, II, II, and IV).\n",
      "\n",
      "(c) Verify that the relationships between the slopes of the order books at-the-money for each parameter set are consistent with the predictions from dimensional analysis.\n",
      "\n",
      "(d) Verify that the asymptotic book depths are consistent with the predictions from dimensional analysis."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# Figure 2: Average book shape (This take some time to run!)\n",
      "\n",
      "logging <- F # Very important for speed!\n",
      "\n",
      "alpha <- 1\n",
      "mu <- 10\n",
      "delta <- 1/5 \n",
      "initializeBook5()\n",
      "# Burn in for 100 events\n",
      "for(count in 1:100){\n",
      "  generateEvent()\n",
      "}\n",
      "numEvents <- 100000 # Average over 100,000 events\n",
      "avgBookShape <- bookShape(20)/numEvents\n",
      "for(count in 2:numEvents){\n",
      "  generateEvent()\n",
      "  avgBookShape <- avgBookShape+bookShape(20)/numEvents\n",
      "}\n",
      "\n",
      "plot(-20:20,avgBookShape,main=NA,xlab=\"Relative price\",ylab=\"# Shares\", col=\"red\", type=\"b\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAIAAADytinCAAAgAElEQVR4nO3dd0DU9eM/8Oext4io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\nJxCKDMO5AAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(c) The slope of the book is around 0.5 , while the dimensional analysis is $\\frac{\\alpha^2}{\\mu\\,\\delta} = 0.5$\n",
      "\n",
      "(d) The depth of the book is around 5, while the dimensional analysis is $\\alpha/\\delta = 5$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# Figure 2: Average book shape (This take some time to run!)\n",
      "\n",
      "logging <- F # Very important for speed!\n",
      "\n",
      "alpha <- 1\n",
      "mu <- 8\n",
      "delta <- 1/5 \n",
      "initializeBook5()\n",
      "# Burn in for 100 events\n",
      "for(count in 1:100){\n",
      "  generateEvent()\n",
      "}\n",
      "numEvents <- 100000 # Average over 100,000 events\n",
      "avgBookShape <- bookShape(20)/numEvents\n",
      "for(count in 2:numEvents){\n",
      "  generateEvent()\n",
      "  avgBookShape <- avgBookShape+bookShape(20)/numEvents\n",
      "}\n",
      "\n",
      "plot(-20:20,avgBookShape,main=NA,xlab=\"Relative price\",ylab=\"# Shares\", col=\"red\", type=\"b\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAIAAADytinCAAAgAElEQVR4nO3deUCUVcMF8DMwgCwq\noCkoKogoKJKVu6mYO7iTiqam5lKmZeZnmaml5VvZ+qa2afq6pJUV5b4vuCHmkooriqwuLIoo6zDf\nHzM5gsMizMy9M3N+f80MM/c5EB0e79y5j0KtVoOIiORjIzoAERHpx4ImIpIUC5qISFIsaCIiSbGg\niYgkxYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIs\naCIiSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIU\nC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgiYgk\nxYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIi\nSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgiYgkpRQd4PGkpaX9\n/vvvarVadBAiIgBwcHAYPny4nZ2dMQY3szPoXbt27d27V3QKIiKtH374IT4+3kiDm9kZNIAOHTpM\nmDBBdAoiIgA4evSo8QY3szNoIiLrwYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCKy\nSvfuISlJdIgymN8HVYiIKqWgAFOn4to11KyJa9fw0Udo3Vp0Jv1Y0ERkZRYuRGAgFi0CgNu3ERqK\n7dvh7Cw6lh6c4iAiK7NnD8aO1d52dcVzz+HECaGBSsSCJiIrY2+PggLd3ZwcODqKS1MaFjQRWZnB\ngzFzprajT5/G0aMIChKdST/OQRORlXnxRdy9i5AQAKhVCytWwDi7OVceC5qIzFlaGv78E/fu4bnn\n0KxZeV81eTImTzZmLMPgFAcRma3TpxEaCkdHNGyIuXOxeLEBxvzpJ/TsiR49MGwYLlwwwICVwDNo\nIuuWnIxZs5CSgsJCPPccZsyAjXznbQkJWLcOOTkICcEzz+genz0ba9fCxwcAevdGly4YO7a0d/xO\nn0ZmJjp0KPEJERHYuRMbN8LODufPY/Ro7N4t8C1E+f5LEJEpjRmDCROwdSu2bUNuLr78UnSgRxw+\njJEj4e2Np57Cxx/jxx91X7p9W9vOAGxs0KIFLl8ubajJk1GvXmlPWLMGH3+snZL290e3boiOrmT8\nymBBE1mx+Hh4eqJdOwBQKDBnDjZtEp3pEXPnYv16DB6MPn2wdi1+/BEqlfZLjo5ITdU98/RpeHuX\nNtQff6B+/dKekJMDJyfdXWdnZGdXNLcBsKCJrFh2NhwcdHcVCl33GUNhIZYuRbdueO45fPstCgvL\n9ar8fNSsqb1tawt/f1y7pr379tsYPBhRUTh3Dm+8gdatUbVqaUO5u5dxrG7dsHSp9nZWFjZsEPsp\ncM5BE1kxPz+cOoWUFHh6AsD69Xj6aSMe7pNPcPcu/vgDNjb47DPMm4f33iv7Vfb2uHMH1asDgFqN\nS5d00xSdO2PJEqxZg3v30K0bQkOLvLCgAIcO4c4dtGmDWrXKlVCzuiM0FLVr4/JlzJ0LN7fH+Q4N\njAVNZMVsbLBoEcLD4eODzEzY22PZMgMMu3UrNm+GQoGBAxEcXOTxPXugUADAnDkIDoZarb2bk4N5\n8/D331Ao4OuLDz7QNeM772DwYMyYAUdH/PgjBg0qsmw5IAAffKAnw40bCAtDjx5wd8fXX2P0aAwf\nXnZyW1t88w2ys5GWBi+vCn77hsOCJrJuLVti3z6kpMDFpYz5gWL278dff0GpxIgRCAzUPf7NNzh+\nHK+9hsJCLFyIxESMGAEABQWws9PWsYaLC+7f1+5S9O678PPDggUAsHEjJk3C2rXap3XujFq1sGoV\ncnLwwgt47rlyxZs1C59/rp2gmDgRXbuif//y7ojk6ChDO4MFTUQAtFMc5bd4MaKi8NpryM7GjBmY\nPFn7wTwAP/2Effu0a/VWrEDXrtqCViqhViMpCXXrAsDNm8jK0jXm8eP49FPt7T59tKexD9a3BQRo\nu7v8YmN108d2dmjfHmfOoE2bxxtENAEFfevWLTs7O1dXV9MfmogeQ14eli7F9u2oUgUjR+pmeAsL\nsXo1Dh7UtvBTT6FPH21B370LNzfdSmqlEnZ2KCiAUgkAX3yBoUMRHAwbG+zejf/+V3cstbrIoe3s\nkJtbqQXITk64fRsPeubqVdSpU/HRBDHFKo5evXrduHEDQFJSUocOHTw8PGrVqtWtW7eUlBQTHJ2I\nKmjKFOTkYN06LF6Mn3/GqlXax2/ehLe3roVdXHQTF1WrIjUV9+5p796+jfx8bTsDaN4c27ahc2d0\n6ICtW4u8Ienlhf37tbcvXEB2Nip5Dvfqqxg1Cteva//MqNVlrICWkinOoLdt25adnQ3gzTffbNiw\n4fbt2+3s7GbOnDl58uTffvutpFclJSWdO3eu2IPHjh1zeniVYgVkZeHrr3H6NPz88PrrZS+7IbIA\nBQVYuRJ798LVFWPHokWLsl9y7x4SEvDddwBQpQqWLUOvXhg5EgBq10Z8PPLyYG8PAOnpRd61mz0b\n/ftj3DgUFGDZMsyfX2RYZ2d0767ncP/9L8aPx5IlsLNDWhq+/76i3+q/QkLg6Ijp03HnDrp0wf/+\nV9kBRTDpFEd0dPTmzZudnZ0BzJw5s1GjRqU8+dq1a3///XexBw8fPlz1sd7HKOb+ffTti4kT8dJL\nOH0a/fsjIgI1apT9wuPHtfsT5uTglVe0c2oa0dF4/33k5UGlQt++mDq14vGIjERTygsXIjUVr7+O\nuXPRsWMZL7lxo8jEtJ2dbtmyQoFXX0X//pg0Cbm5+OILfPKJ7pm9e6NpU2zeDBsbrFlT3okFNzes\nX4+MDBQU4IknHuubK1GXLujSxTBDCWKigk5OTvby8mrWrFlcXFyTJk0AnD17tnbt2qW8pH379u3b\nty/24PXr18s1MRIfjy++wPnzaNIEb7yBBg20j0dEYOBAhIcDQNeuSE/H8uWYPr2M0TIyMG0a1q2D\nhwfy8jBuHOrW1f6Hv3MH06bhl1/g6QmVClOn4tdfMXhw2QmJTCYpCXl5mDYNAGrXxs8/Y+zYsgva\n2xtnzuDePe37eDExRU5lhg9Hs2bYvRu2tlizpvjn9xo0wCuvVCSq0EXHEjJFQXfq1Ck8PPzmzZuO\njo7x8fE9e/bcv3//gAEDPv74Y6McLzUVQ4fiyy/RqhWOHcOwYfjzT+3f5Ph4PPWU7pkBAYiMLHvA\nffsQFgYPDwCwt8fs2fjsM21BHzqEfv20Jxq2tpg9G6+99hgFnZQEV1fBF0NLTcWuXQDQrVu5/jFB\nZic+Hg0b6u7WqIHMzLJfZWODBQvQvz/69cO9e9ixo/gswZNP4sknDRyVijLFm4T79u2Lj4/PzMyM\njo7+5ptvADg6Om7YsGHChAlGOd769XjtNbRpAxsbtG6NN97Azz9rv/TUU9izR/fM3buL9HVJ7t8v\n8nFYBwfcv6+9rVIVWddZ/k/K7t+Pzp3x7rsID8fo0cjLK9erACQkYPVq/P677n2Yyjh8GIMGIS0N\n9+5h8GAcOWKAMUk2TZviwAHdBEV0dBkbVjzQtSt++QWNGqFNG2zdao5vspk7081B29vbN2rUSDPv\n3KpVKyMeKTkZTZvq7np56a4I2bMn1qzB66+jfXucPImzZ/H772UP2LEjRo/GqFGoUgUAlixB797a\nL7VrhwUL8NJL2n+affop+vYte0DN0tEtW7Sv+v57fPwxZs8u+4W//YblyxEejuvX8dxzWLkSTZpo\nv1RYiBUrsGED7O3x0kvo0aPs0QC89RYiIrTvlPbrh7Aw7NtXrheSGaleHeHhGDQIgwcjNRVr12L9\n+vK+1t1dt8CZTM4SP6jSujU2bECnTtq7f/2Ftm11X125ElFROHsWvXtjwYIi578lqVcP06ejc2d4\neSEpCaGhGDZM+6UaNbBgAZ5/HtWr4/ZtdOqEUaN0L1SpsGwZTp5E1aqYOFH3z8xTpxAcrJtuGztW\n1/ilyM/HJ58gMlL71nm3bnj7bd0fmP/7P1SvjuXLkZWFmTNx44b2DXeNGzewezeUSnTvrlu9pNm4\n68E6lpo14eiI3Nwi/1xIT0dhoW6rGjJTkyahZ08cPAgfH+zdqz3VIOlZYkH36YOICLz0knYOWq1G\nv35FntCmzWN/oKh3b/TsiaQk1KpVpL8ABAcjOFj7mahidf/ii2jVCq+/juvXMWYMvvsO/v4AtD34\nQF5ekVVKN2/irbcQF4f8fAwbhldf1T4eG4unn9a2M4DGjZGRob2dk4MTJ7B7NwC4umLZMvTooSvo\n3bsxbx4GDEB+Pvr2xeLF2ktkVqmC+/dRWKhd0FpYWGQyJyUF48ahWjXY2uLGDXz3XZF5TDI7vr7w\n9RUdgh6PJRY0gKVLERODCxcwbVqR6Y7KsLEpbQ7OxaX4I+fPw8EBr78OAE2a4Lvv8Mkn2r3GmzXD\niRM4dQpPPgmVCjNn6t5XVKsxfDjefx8dOiA/H+++iyVLMGkSANSti7g43fj37+tqPTVV+/FZDXv7\nIn8q3n0X27Zpt1kYMQLjxun2/B00CC+/jNmzoVZj3rwib2++8QbmztV+WPb8eUyZIuNOwUQWzUIL\nGkDTpgar5oqJjdWeL2v4+ek2sVUqsXw5Zs/GzZsA0LcvxozRvapBA+0leezs8OGH6NVLW9BVq8LP\nD++/j4kTkZmJN9/Ea69pX1W3Lq5cQVaW9u9EbKxuHiM9HR4euk1wPD2Rk6PbQmzqVGzciHnzACAs\nTDfTolbj1i3dVgb+/rC11Y1P0jp2DAcOoEYNDBzI/1gWwHILugJSUvDhh7h4EbVr4623imzQVQHN\nmuH77/F//6e9e+gQAgJ0X/XxwerVel6VnV3k/yulssim5l9+iZ9+wttvw8kJs2bp5tYVCsyejdBQ\nDBqE7Gz89ZduRZSrK9LSdCOoVMVXnvTpgz59isd4dDlKTo5udkXj9m3k5ZV3m10ygXffRUoKnn8e\n16+ja1f89pskW7JRhbGg/6VZZzZ/Pjp1QkwMJk7EqlWVmnX19sYzz+DFFxEWhitX8Pvv5XrrPCAA\nf/+Nmze1xffrr3h4xYuNDUaMKPI5xgd69UKbNjhyBPb2eOMN3VSyjQ26d8fMmZg8Gfn5WLCgyNuY\npQgKwg8/YPx4APj9d9SqpSvotDSMHYsqVeDggKQkLFpU5G8PCZGYiBMndNNQTz6JefMM8IFpEooF\n/a+tWzF4sPbjJ82b4z//wfLlxbcReFxz5uDYMURGolYtbNtWrq25lErtWr2AAGRkQKnUf6Ktl5ub\n/tUgs2ZhzRpMmQKlEiNHlmshIICPP8bcuejZEwoF/PyKXNB++nRMm4bOnQHgyhVMmICdO8sbkowk\nJqbIxaqffrqMy6eSOWBB/yslpcj7bF5eSE42wLAtW6Jly8d7Sdu2OHAAKSmoUsUwEwgKRYnn3aVw\ndCyywcLDrl3TtjOAhg1RowZu3TLY/glUMb6+RS53ff68Oe6uScXworH/0qyefuCvv0Tu7W1nh/r1\n5Z3eLXatz/v3ua5WPF9fODjgww9x4QL27cOYMXj7bdGZqLJ4Bv2v1q2xbRsGDEDXrjhxAgUFWL5c\ndCZZtW+PL77AG28AwJYtsLd/vEslkZEsX47167F4MWrUwLp1uj3CyGyxoB8yezZiY/HPP+jYsVwb\n5lqt997D/Pno0QM2NvD25jtRsrCxwZAhGDJEdA4yGBZ0Ufy0VXnY21f27VMiKgfOQRNZBM3Fpciy\nsKDJEDSfYySBJk1CQoLoEGRgLGgyhPPn8dZbokNYsatXcf8+d7OyPCxoMoSQENy6hcOHReewVkuW\nYPJk0SHI8FjQZCALF2LrVtEhrFJWFqKi0K2b6BxkeCxoMpAGDfD++6JDWKWVK/HCC6JDkFFwmR2R\nOSssxKpV2sv+ksVhQZOhpafjjz+QnY3u3XWXTCQj2boVnTrByUl0DjIKTnGQQZ07h379UFCA6tUx\nfTp++kl0IEu3fDkmThQdgoyFZ9BkUO+8g7VrtdcGGzYMwcEYMgRK/poZzXff6S77SxaHZ9BkULdv\n667cqFQiMBCxsUIDWTq2s0VjQZNBaS5d+MClS7zqElGF8d+eZFBvvonwcMydC2dn/O9/aN0azs6i\nM1mWggIsXYp//kG1anj5ZXh7iw5ERsSCJoPq3Ru1amHpUuTkICQEgweLDmRxhg9HmzZ4/XUkJmLo\nUKxZg0aNRGciY2FBk6E98wyeeUZ0CAv1zz9wd8ebbwJAkyb4/nt8+im+/VZ0LDIWzkETmY/Y2CIX\nUA8IwNWr4tKQ0bGgyZjy85GRITqEBQkMRGSk7m5kJJo1E5eGjI5THGRMiYnaldFkEH5+CAjA2LEY\nOBCXLuGvv7B+vehMZEQsaDImHx+o1bh0CX5+oqNYivnzERWFQ4fg4YGtW3k9dcvGgiYje/NNfPkl\nFi8WncOCtGmDNm1EhyBT4Bw0GVmrVrh8GamponMQmR8WNBnfpElYskR0CIuwfTsKC0WHINNhQZPx\n9euH3buRnS06h5m7cwfz5kGhEJ2DTIcFTcanUGDIEK7lqKzFi/Hqqyxoq8I3CckkXnoJSUmiQ5iz\n7Gxs2oT9+0XnIJPiGTSZhIMDGjYUHcKcrVqF4cNhays6B5kUz6CJpFdYiJUrsX276BxkaixoMqEb\nN7BmDe7eRY8eaNdOdBrzERGBXr144UErxCkOMpXTp/H886hXD927Y8UKLFwoOpD5SE3Fyy+LDkEC\n8AyaTOXdd7FmDerXB4D27dGlCyZMQPXqomOZgwkTRCcgMXgGTaaSmaltZ42WLXHpkrg0RGaABU2m\nUr06UlJ0d0+d4g5KpVGrkZCAnBzROUgkTnGQqcyZg0GDMHs2XF2xYgU6dOD8RokiIvD55/DzQ2Ii\nAgPx6af8fIp1YkGTqTz9NNavx88/4+5djByJjh1FB5JVcjIWLcL27dqtROfPx4oVGDNGdCwSgAVN\nJlS3LqZNEx1CegcPIixMt9HzxIl47TUWtHXiHDSRZBwdkZWlu5uVxRXQVosFTSSZjh3x55/aq8Hm\n5GDWLAwfLjoTicGCJhHS0zF2rOgQsqpeHcuX4+230aMHBgzA0KHo1k10JhKDc9Akgrs7Ll1Cfj7s\n7ERHkZKfH37+WXQIEo9n0CRIx444eFB0CCKpsaBJkD59sHGj6BBEUmNBkyBt2+LoUdEhZBUbi9hY\n0SFIPBY0CWJjAx8fbseh37JluH5ddAgSjwVN4oSGcpZDv2PH0LKl6BAkHguaxOnVi1cJ0UOzQZKD\ng+gcJB4LmsSpVg1qNW7fFp1DMtHRaN1adAiSAguahOrRAzt2iA4hmchIPPus6BAkBTEFfeTIkdzc\nXCGHJrn0789p6OIOHUL79qJDkBTEFHSfPn1u3bol5NAkF19fxMZCpRKdQxoqFbKyUK2a6BwkBVMU\ntIuLi7KotLS0Bg0aKJX8oDkBbdsiKkp0CGmcPo2gINEhSBamqMjo6OiXXnrJy8vro48+qlatGoDG\njRvv3bu3Tp06pbzq9OnThw8ffvRBR0dHI2Yl0wsNxaZN/Ee9VmQkL2VAD5jiDDogICAyMrJ9+/Yh\nISFHjx6tWbOmjY2Nu7t7zZo1S3mVnZ2d2yOqVKmi4LV/LEzHjjhwQHQIabCg6SEmmmSwtbWdOnVq\n3759x40bt3bt2ry8vDJf4u/v7+/vX+zBQ4cOpTx84VGyAEolPD0RFwdvb9FRJJCcDA8P0SFIFiZ9\nk9DX13fXrl0dO3YMCQnhTAXp9O6NrVtFh5DA5cu80jk9zNRv09nY2EyYMGHChAkmPi5JLSwMiYmi\nQ0iAK6CpKH5QhSTg4oJHprOs0YEDnICmh7GgiaRx8SKnOOhhLGiSRlYWkpNFhxAnJQW1aoGLlOgh\n/KgISSA3FxMm4PZtuLvjyhV8+KE1TsUePMj5DSqGBU0S+M9/0LUrRo0CgPR09OuHnTtRpYroWKYV\nGYmRI0WHILlwioMkcOAAXnhBe9vdHc8+i1OnhAYS4dQptGghOgTJhQVNElAq8fBnl7Ky4OQkLo0I\nd+7A0RHcnYaKYkGTBIYOxcyZ2j3tTpxATAyaNhWdybSOHEG7dqJDkHT4F5skMGYMfvgBvXtDoUCd\nOvjpJ9jais5kWpGR6NpVdAiSDgua5DB+PMaPFx1CnKgozJolOgRJh1McRKLl5yM/H9ydhh7BgiYS\nTaHA55+LDkEyYkGTZB65SoPlUyrx9NOiQ5CMWNAkmXfeQWGh6BBEUmBBk2QaNcLly6JDEEmBBU2S\nad4c//wjOoRJ7N2Ljh3RtStat8a334pOQzJiQZNkgoJw+rToEMZ3/To++ACbN2PXLhw8iEOHsHOn\n6EwkHRY0SSYoyCrOoHfvRng4qlYFADs7vPMOfv9ddCaSDguaJOPujvR00SGMT6UqsvWzQqH9pDvR\nQ1jQJB8XF2Rmig5hZF26YPVq3L0LACoVPvsM/fuLzkTSYUGTfJo3x9mzokMYmZcX5sxBr17o1w/t\n2uHppxESIjoTSYd7cZB8NAs5LH53ty5dcPAg7t7VzkQTPYJn0CSf5s2tYiGHBtuZSsaCJvkEBODC\nBdEhiMRjQZN87OyQmwu1WnQOI9uxQ3QCkh0LmqTUoAESEkSHMCa1Gu+9JzoEyY4FTVKy+GnoEyfw\n1FOiQ5DsWNAkJYvfkWPLFvTuLToEyY4FTVKy+B059uxBly6iQ5DsWNAkpbp1kZQkOoTRpKfD3h5O\nTqJzkOxY0CQre3vk5ooOYRw7d6JHD9EhyAywoElWTZvi3DnRIYyDE9BUPixokpWlvk+oVuPSJTRp\nIjoHmQEWNMnKUt8nPHkSTz4pOgSZBxY0ySowEGfOiA5hBJzfoHJjQZOsnJxw757oEEbABXZUbixo\nklitWrh5U3QIg0pPh1IJZ2fROcg8sKBJYpb3ge9du7jAjsqPBU0Ss7wLyHICmh4HC5okZmELOdRq\nXLwIf3/ROchssKBJYj4+uHpVdAjDOXUKQUGiQ5A5YUGTxGxsAEClEp3DQDi/QY+JBU1ya9wYly6J\nDmEgBw4gOFh0CDInLGiSmyUt5Fi1ipeIpcfCgia5WVJBu7uLTkBmhgVNcrO8lXZE5aYUHYCoVG5u\nyMgQHaJyLl/G6dPw9eUSDnpcLGiSXtWqyMxEtWqic1TI3Lk4fRpduuDPP2Fjg6VLtUtTiMpB/+/K\n5cuX8/LysrOzFy1a9OOPP+bn55s4FpFO8+bmuq3dwYNISsLvv2PKFKxYAX9/rFwpOhOZEz0FPW/e\nvMDAwMzMzE8//XTVqlVfffXV66+/bvpkRFq9e5vrWefRo+jbV3e3Xz9ERYlLQ+ZHzxTHV199deTI\nkRo1aixZsiQqKqqgoKB169ZLliwxfTgiAOjUSXSCivL0LHLp28RE1KkjLg2ZHz0nJiqVytXVNTo6\nunbt2vXr13dycsrLyzN9MiKz16cP1qzBvn0oLMSpU5g7Fy++KDoTmRM9Z9Dh4eG9evXKz8+fNWvW\n1atXhw0b1r17d9MnIzJ7Li745Rd8+CE++ACenli6FPXri85E5kRPQS9atOiPP/4AMGjQoCtXrgwe\nPHjixIkmD0b0r/h4rFiBW7fw7LMYPNjM5qPr1gWnB6mi9BS0UqkcPHiwSqW6efNmo0aN3nzzTdPH\nItKKicHYsfjoI3h64rff8OKLWLVKdCYiE9FzMpKUlNSlS5dq1ao1bdr077//7tix41VL2vKRzMsn\nn2DZMgQHo0kTvPMOVCpcvCg6E5GJ6CnoMWPGBAYGpqWlVa9evUWLFm3bth0/frzpkxEBQEICAgJ0\nd1u0QGysuDSP7/x5HD4sOgSZKz0FfeDAgfnz51epUgWAUql86623DvM3jERp0gR//627GxmJZs3E\npXl8v/2GzEzRIchc6SloPz+/AwcOPLgbFRXVsGFDE0YiesisWXj1Vfz4I7ZswfjxCAoys4UQR4+i\nVSvRIchc6XmT8L///W9YWFhwcHB6enpYWFhkZOTq1atNn4wIAOrWxe7d+OMPnD+PCRPMr+zS07nL\nKFWYnoLu3LnzhQsXNmzY0KJFC09Pz8WLF3t4eBjwkLm5uUql0tbW1oBjkiVzccHIkaJDVEhcHHx8\nRIcgM6ZniiMoKOj69eujR49+9913X3rppcq3c0xMTEhIyOjRo+Pi4jTrQ1xcXMLDw1NTUys5MpHU\noqLQpo3oEGTG9BT0kCFDPv3009zcXEMdY/z48Z6ennXr1m3VqlWrVq2Sk5MvXrzo4OAwZcoUQx2C\nSEYsaKochVqtLvZQcHDwyZMns7Oz69Wrp1Rq50DOnz9f4WM4OjrGx8fb2dm5ubndu3fPyckJwK1b\ntxo3bpxR8l7se/bsWbduXbEHDx8+XKdOna1bt1Y4DJmxyZOxaJHoEI+jWzds2QI7O9E5yIjGjRs3\nc+ZMX19fYwyu/6Pehj1GtWrVUlNT/f39161bp2lnALGxsXXr1i3lVUFBQdUe2aM9KyuLOzdZr4QE\npKWhRg3ROconLw9qNduZKkNPQQcGBhZ7ZNWqVY8+WH4TJkzo1avX+vXrhw4dCiA+Pv7zzz9fu3bt\nxx9/XMqratSoUeOR/xVr1aqVkpJS4SRk3jQ793fuLDpH+Zw+zWtcUSXpKejz589/8cUXd+7c0dzN\nzs6OiooaWYm30efNm9e5c+eaNWtq7ubk5NSpU2fTpk0tW7as8JhkjTRX+DaXguYENFWanjcJR40a\nlZeXV69evbt37/bp0+f69evLli2rzDEUCkW3bt18/l1v1Lhx4xkzZrCd6bFpCtpcsKCp0vScQf/z\nzz9btmypUqXKgAEDRowY0b179+effz40NNT04YiKaNwYly6JDlFuXARNlabnDNrDwyMmJsbZ2Tkj\nIyMjI6NatWoxMTGmT0ZUnFKJ/Hw8su5IRpjLwqcAABk8SURBVBkZqF5ddAgye3rOoN95551u3bpd\nunSpd+/e3bp1c3Fx4XQEycLbG9euwdtbdI6yREejdWvRIcjs6SnoCRMm9O7d+4knnpg7d25AQEB6\nevqoUaNMn4xIj8BAnDljBgUdFYW2bUWHILOnp6AB1KtXT3Nj+PDhJgxDVJbmzXHqFPr0EZ2jLNHR\neO010SHI7Okp6F27dr333nvFPuN35swZU0UiKlnz5jCLvRVv3+YcNFWenoIeO3bs+PHjBw0aZGNe\nV+cka1CvHhITRYcoy5Ur4BbqZAh6CjonJ2f69OmaK6oQSUepRF4e7O1F5yjZkSNcAU0GoeccefLk\nyV999ZVKpTJ9GqKy+fvjwgXRIUrFj6iQgRQ5g/b39wegVqsvXbq0YMECDw8PhUKh+VJldrMjMiTN\n5wmbNxedo2SSxyPzUaSgIyIiROUgKq/AQGzZIjpEyXJzoVBwEzsyiCJTHP7+/k2aNPHw8PD39/f3\n98/MzNy/f7+tra3mzJpICpql0NI6dQotWogOQRaiSEFfunQpMDBQs3Hd0aNHO3XqtHbt2pYtW27b\ntk1QPKJHuLmh5Os8iMcJaDKcIgU9bdq00NBQzUTHnDlzvv322z179nz00Ufvv/++oHhE+lSrhsxM\n0SFKwIImwylS0AcPHpw2bZqtre39+/ePHTs2bNgwAM899xw/pUJykXmW49o1NGggOgRZiCIFrVKp\n7t+/D2Dfvn2tW7d2cHDQPO7s7CwgGlFJpN0YOjXVbK7IReagSEG3bt36xx9/vHv37pdfftm3b1/N\ng2vWrGnVqpWIbEQlkLagT53iJnZkQEWW2X322WehoaEffvhh8+bNx44dm5OTExoaevz48ejoaFH5\niPTw94ecC/ODg83milxkDoqcQQcFBcXFxV27du348eMODg42NjZjx469ePFio0aNROUj0sPBATk5\nokPoY2sLpf4dIokqoPgvk62tbf369TW37e3tX3jhBZNHIiqHunWRnIw6dUTnIDIi7ldH5km2aejk\nZOzdawY77ZFZ4T/HyDxpCrpnT9E5AAAffojISAQF4exZBAXhP/8RHYgshJ4z6C+//FJzI5GnAyQt\nec6gDx1CfDy2bsUnn2DTJuTng5+8JQPRFfSyZcteeOGFBQsWfPTRR3FxcYWFhc8++6zAZESl8fbG\n1auiQwAA9u3D88/r7g4Zgt27xaUhi6Kb4ujfv3/dunXPnj17586dwYMHJyYmpqWljRo1qkmTJk2a\nNHn+4V9BIuFsbGBjg4IC8asm3NyQnq67m5YGV1dxacii6M6gk5KSqlatOm7cuNq1a0dHRyclJT3x\nxBPh4eHOzs67eUZAEvLzw+XLokMAgwbhm2+0SeLjsXAhhgwRnYkshO7s48aNG99+++2ZM2eSkpJ6\n9eoVGBiYm5tbs2bNdu3aubm5CYxIpJ9mRw7he+HWqoUlSzBjBhITUbs2Pv8cvr6CI5Gl0BV0jx49\nevToAcDLy+uDDz44c+ZMXl7ee++9d/HixXv37qWkpIgLSaRP8+bF539FadoUv/8uOgRZID3zd59+\n+mnLli1btmz5008/bd68GUBeXp7JgxGVJSgIixaJDkFkRHqW2YWHh2tubN++XXPDXuYrKJPVqlkT\nt26JDkFkRPwkIZkzJyfcuyc6BKBWY8cO0SHIArGgyZw1a4aYGNEhgNhY/PST6BBkgVjQZM4CA3H2\nrOgQwNmzaNZMdAiyQKIX+RNVxtChyM0VHQKIieGVvMkYeAZN5szZGe7uokMAZ8+iaVPRIcgCsaCJ\nKi0+Hv/uok5kQCxoMnNqNbKyRAZQqaBQQKEQmYEsFAuazNlHH6FtWwwbhs6dIerKmVev8rPdZCR8\nk5DM1v/+h9u3ceQIFAqkpWHAAPz1F0y/bwwnoMloeAZNZmvDBvzf/2nnFmrUQL9+OHRIQAyusSOj\nYUGT2bK1RWGh7m5hoZi9oWNiWNBkJCxoMlsDB+KDD7QdnZyMjRvRrp2AGPHxqFdPwHHJCnAOmsxW\neDiSk9G9O2xt4eCAL79EtWqmzsAlHGRMLGgyZ9OmYdo0kQGuXOESDjIeTnEQVUJMDJdwkPGwoIkq\ngUs4yJhY0GQRrl4Vc1wWNBkTC5oswujRYo6bkMAlHGQ8LGiyCPb2uH/f1AdVqWBjwyUcZDwsaLII\nTZrg0iVTH/TKFTRsaOqDkjVhQZNFaNIE58+b+qCcgCYjY0GTRfD3Z0GT5WFBk0Xw98eFC6Y+KBdB\nk5GxoMkieHkhMdHUB+USDjIyFjRZBM1Sioc3tzM2LuEg42NBk6Vo0AAJCaY7HHfhIONjQZOlMPFC\nDl5IhYyPBU2WwsQLObiEg4yPBU2WwsQLOXghFTI+FjRZCj8/k36YMDERXl6mOxxZJdMVdEZGhlqt\nfnBXpVKlpqaa7Ohk+RwckJtromPxQipkEqYo6LNnzzZr1qxGjRqNGjXauHGj5sGEhIQnnnjCBEcn\nK1K9Om7fNsWBYmO5hINMwBQFPXHixLCwsJycnOXLl7/88svHjh0zwUHJGplsGprvEJJJmOKahCdO\nnNi8ebO9vX2nTp0WL1788ssvR0VFlfmqX3/99fvvvy/24MWLFxs1amScmGT+NCvt2rQx+oFiYvDM\nM0Y/Clk9U5xB+/n5bd++XXO7X79+9erVmzNnTpmvGjx48I5HDBo0iBMjVCKeQZNlMUVBL1y4cMyY\nMe3atbt586ZCofjhhx+2bNkycOBAExyarIvJlkInJXEJB5mAKaY4unfvfvHixf379zs6OgKoWbPm\n4cOHIyIijh8/boKjkxWpWRMmWBrEXTjIVExR0AA8PT2HDh364K6Dg8PQoUMffoTIMJRK5OfDzs6I\nh4iN5YVUyDT4QRWyLL6+uHLFuIfgBDSZCguaLEuTJjh3zriHYEGTqbCgybKY4H3C8+cREGDcQxAB\nYEGTpTHBSrt330X9+sY9BBEAFjRZGh8fXL1q3EP4+xt3fKJ/saDJstjaoqBAdAgiw2BBk8Xx9MT1\n66JDEBkAC5osjpHeJ/zlF7Rti65d0a4d/vzT8OMTPcJEH1QhMh1NQQcHG3LMU6ewejV274aTE7Ky\nMGQIGjfmWg4yNp5Bk8UxxkKODRswdSqcnADAxQWTJ2PTJgMfgugRLGiyOMYoaM0lVB6wsYFKZeBD\nED2CBU0Wx9kZWVkGHjMkBIsWIS8PAHJysGQJevc28CGIHsE5aLJEjo64f187I2EQrVph6FB07AgP\nD1y/jpkzERRksMGJSsCCJkvUpAkuXkSLFoYcc8gQDBmCu3dRtaohhyUqGac4yBJprn1lDGxnMiEW\nNFkik11ahciYWNBkiYy0ZVJcnOHHJCoZC5osUd26SE428JixsXj/fQOPSVQqFjRZrsJCQ4525gz3\n6ScTY0GThWrQAPHxhhwwJgZNmxpyQKKysKDJQhl8IQcLmkyOBU0WyuALOeLj0aCBIQckKgsLmixU\nQIAhL62imc5+eDsOIuNjQZOFatoUn3xisNGuXoWPj8FGIyofFjRZLgcHgw3FCWgSgQVNVA5nz7Kg\nyfRY0GS5UlPxzz/IzjbAUDExXARNpsfd7MgSFRZi4kRkZMDbG3//jTFjMGpUpQa8do1LOMj0WNBk\niZYuhb8/3nwTAFQq9O2LTp3g7V3B0QoLoVbDhv/cJFPj7xxZor178cIL2tu2thg0CAcPVny0a9e4\nhIOEYEGTJapeHWlpurvp6XB1rfhoZ8/yAt4kBAuaLNGIEZgxA3fuAMDZs4iIQOfOFR+N7xCSIJyD\nJkvUoQNefRUjRyInB3XqYOVKuLhUfLSYGISFGS4cUXmxoMlChYQgJMQwQ8XFcQ6ahOAUB1Gp1GoU\nFnIJBwnBXzuiUnEFNInDgiaLVliIqKhKjcBdOEgcFjRZNJUK77xTqRG4CweJw4Imi2Znh4KCSo1w\n7hzX2JEoLGiydFWqVGq/pCtX0LCh4dIQPQYWNFk6Hx/ExVXwtWo1VCou4SBR+JtHls7HB1euVPC1\nCQmoX9+gaYgeAwuaLF3DhoiNreBr+Q4hCcWCJkvXsGHFrx7LXThIKBY0WbqGDSs+xcFF0CQUC5os\nnZsbMjIq+NrYWPj6GjQN0WNgQZN1UKsr8hKVCra2RkhDVC4saLICnp64ceOxX5WYiHr1jJCGqLxY\n0GQFKjYNzQloEo0FTVagYkuhWdAkGguarADPoMk8saDJClSsoC9fRqNGRkhDVF4saLIC9esjPv7x\nXqJWIz8fSl4TjkRiQZMVUCofe9PR5GR4eRknDVF5saDJOjzupqOcgCYJsKDJOjzupqPcJokkwIIm\n6/C47xNymySSAAuarMPjFrStLZdwkHAsaLIOj7vp6DffwM7OaGmIyoUFTdahMpuOEgnCgibr4OaG\n9HTRIYgeD9fhkzVRq6FQlPGE/fsRG4vmzdGqlaliEelnioI+f/58SV/y9/c3QQAiAPDwwI0b8PAo\n8Qn5+RgwAC1aICgIK1diyRIsX27CfETFmaKgp02btmXLFicnJzc3t2JfSkxMLOlVv/3227ffflvs\nwdjY2MDAQMNHJGugmYYupaBXrkTv3pg8GQCGDsWMGdixA927mywgUTGmKOjNmzePHz/ewcFh0aJF\n5X9VWFhYWFhYsQd/+eWX1NRUg6Yjq6HZdLR9+xKfcOIEXnlFd/e553D8OAuaBDLRm4Th4eHe3t6m\nORaRfr6+ZSzkqF8fFy7o7p4/jwYNjB2KqBQmepOwa9euXbt2Nc2xiPRr2BBr1pT2hLFjMWAA3NwQ\nFIQDB7BhAzZuNFU4Ij24zI6sRpmbjtasiT//xJ49mDIF587hr7/g6GiqcER6cJkdWY3ybDpaowbm\nzTNJGqKy8QyarImDA3JyRIcgKi8WNFmTx910lEgoFjRZEx8fxMaW9oS33jJVFKKysaDJmpS+ZVJC\nQhn1TWRaLGiyJqVvOrpzJz+WQlJhQZM1Kf0MescO9OxpwjREZWBBkzVxd0dGhv4vFRYiLg78vCvJ\nhAVN1ket1vPgiRN4+mmTRyEqDQuarEzt2rh5U8/j27ahRw+TpyEqDQuarExJ09B796JLF5OnISoN\nC5qsjGbT0WKysqBWo2pVEYGISsSCJivTsKGexc5796JzZxFpiErDgiYro3cp9I4dnIAmCbGgyco0\naKBn09Fjx/DMMyLSEJWGBU1WRqlEfn6RR65dg5cXbG0FBSIqEQuarE+VKkU2Hd2+nfMbJCcWNFmf\nYpuO8hPeJCsWNFmfh1faqVRITISXl9BARPqxoMn6PPxZlWPH0Lq10DREJWJBk/V5eKXd9u3cYpSk\nxYIm6/PwZ1X270dwsMgwRCVjQZP1cXdHjRoAkJcHhQLOzqIDEenHgiartGwZANjbY8MG0VGISsSC\nJuvm4CA6AVGJWNBERJJSig5AZHJqNSIjkZaGoCD4+opOQ1QiFjRZmfx8DBwIX1/4++OXX+DjgwUL\nRGci0o9THGRlli5FaCi++gqvvIK1a3H9Oo4dE52JSD8WNFmZo0fRu7fubkgIjh4Vl4aoNCxosjJ1\n6hTZKenqVdSpIywMUalY0GRlxo3D7NmIikJODv76C5s3cys7khbfJCQr4+ODlSvxySeIi8MzzyAi\nAo6OojMR6ceCJuvj44NvvhEdgqhsnOIgIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIi\nSbGgiYgkpVCr1aIzPIbt27dPnjy5WrVq5XnyuXPnjJ3HjKhUKoVCYWPDP8la+fn5dnZ2olPIoqCg\nwNbWVqFQiA4iC3t7e9/y7RWemZm5d+/eOsbZ0cXMCvqxdOnSZc+ePaJTyGLx4sW1atUaPHiw6CCy\n4K/Hw2bOnNm/f/+2bduKDiKFmzdvTpky5eeffxYdhFMcRESyYkETEUmKBU1EJCkWNBGRpFjQRESS\nsuSC5iKqh9na2tra2opOIRH+ejzMxsaGvx4P2NjYSLIg1ZKX2eXm5jo4OIhOIYuCggKFQsH/CR/g\nr8fD8vLy7OzsuA76AUl+PSy5oImIzJoUp/FERPQoFjQRkaRY0EREkmJBExFJigVNRCQpFjQRkaRY\n0EREkrLAgt65c2eLFi2cnZ2fffbZs2fPah48duzY008/7ebmNmbMmOzsbLEJTS8kJOT8+fMP7lr5\nT8PKv/2H8RdDQ9rSsLSCTklJGThw4KxZs5KTk7t06TJkyBAABQUFzz///KRJk86cOZOQkPDFF1+I\njmk6u3btGj9+/JYtWx48Ys0/DVj9t/8AfzEekLo01JZl3bp1bdu21dzOzc1VKBTp6ek7d+709/fX\nPLhnzx4/Pz9xAU1t4cKFr776qpOT07lz5zSPWPNPQ2313/4D/MV4QObSUIr5s2A0ISEhXbp00dw+\ncuSIt7e3q6trXFxc8+bNNQ82b9782rVrarXaSrYdmD59OoCIiIgHj1jzTwNW/+0/wF+MB2QuDUub\n4qhatWqtWrXUavWff/45fPjwr776SqFQpKamVq1aVfOEatWq5eXl3b17V2xOgaz8p2Hl334prPYn\nI3NpWEJBf/31166urq6urj/++COAtLS0sLCw+fPnR0RE9O3bF4Cbm1tWVpbmyZmZmUql0sXFRWRi\nYyr203iUVf00HmXl334prPknI21pWEJBT5ky5fbt27dv3x47dmxubm6PHj0CAgKioqJatmypeULD\nhg0fvDN77tw5b29vSTZ7NYaHfxp6n2BVP41HWfm3Xwqr/cnIXBqW9h8gIiJCpVKNHz8+ISEhLi4u\nLi5OpVIFBwdnZGSsX78+Kytr4cKFI0aMEB1TJCv/aVj5t18Kq/3JSF0aQt6aNJ4ZM2YU+wZv3bql\nVqujo6OffPJJd3f30aNH5+TkiI5panXr1n3wZr3a6n8aVv7tP4y/GGq5S4Mb9hMRScrSpjiIiCwG\nC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgiYgk\nxYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgSSJeXl6Kf1WtWjU0NDQ5Obmk\nJ588eTIwMLCU0ZRKZUFBwbFjx1q2bGmEsDDeyEQaLGiSy+bNmzMyMtLT048fP56ZmTlr1qxKDujj\n4zNv3jyDZDPZyEQaLGiSS9WqVV1dXd3c3Pz8/EaMGHHlyhXN45GRkU899ZSzs3OvXr2SkpKKveqH\nH37w8fFxdHRs27bthQsXAPTo0UOlUvn6+p45c2bOnDkAevXq9f3332uev3DhwvDw8NKHXb169fjx\n40eNGuXq6tqhQwfNsGfOnAkODv7ggw+CgoKuXr2qGRnAL7/84ufnV6NGjVdeeSU3N7fMwETlwYIm\nSSUnJ2/durVnz54A0tLSBg4cOG/evMTExEaNGo0YMeLhZyYkJEyePPl///tfQkJCQEDA559/DmD7\n9u22traxsbHOzs6apw0YMGDTpk2a2xEREeHh4aUPC2DFihXt2rW7dOnSs88+O3ToULVaDeDkyZOx\nsbFr16598LSLFy9OmjRp5cqV0dHR0dHRq1evLnNkonJRE0mjbt26zs7O1atXr1atGoC2bdsWFBSo\n1eoVK1aEhYVpnpOdne3k5FRQUHDixIlmzZppHrl27Zparc7Kypo+fbqmSdVqta2tbX5+fnR09DPP\nPKNWq5OTk11cXLKzs1NSUlxdXbOzs/UO+yDMqlWrgoKCNLfz8vLc3d0vXrx4+vRpe3v7nJwctVr9\nYOT58+dPmTJF88yTJ0/u27ev9JGJykkp+g8EURHLly9v1aoVgNTU1GHDhq1evfrFF19MSEjYvn27\nt7e35jn29vY3b9588BKlUrl06dItW7ZUr17dwcGhatWqekf29PQMDAzcu3dvfHx8//79q1SpondY\nT0/PBy/x8fHR3LCzs/P29k5KSqpZs2a9evUcHBweHjkxMdHPz09z+8knnwSwf//+0kcmKg8WNMnF\n09NT02ve3t5hYWEnTpx48cUXPT09u3fv/ttvvwFQqVQnTpzw8PC4ceOG5iW//vrrpk2bduzY4e7u\nvnr16o0bN5Y0+MCBAzdt2hQbG/vaa69pjvXosA8//+rVq5obBQUF8fHxnp6e+fn5SmXx/2tq166d\nmJiouX348OHLly+XOTJReXAOmuTl4eGRkJAAIDQ0NDIycvPmzampqW+//fbUqVMVCsWDp6Wlpbm4\nuDg6Ot68efPrr7/Ozs5+8KWsrKyHBxwwYMAff/xx6tSprl27ljksgH/++ee7775LTU2dPXt2nTp1\nHpwmFxMWFrZq1aqoqKgrV65MnTo1NTW1zJGJyoMFTfJq3LjxgQMHMjMzPTw8Vq9ePWPGjAYNGvz9\n998rV658+GkjR450cHDw8vIaOHDg7Nmzo6KiVq1aBSAsLKx+/fr37t17eMDq1av37dvXzs4OQOnD\nAggJCdm5c2fDhg337t27bt06Gxv9/78EBQV9/vnnw4YNe+qpp5o1a/bqq6+WOTJReSjUarXoDEQy\n0syWrFu3TnQQsl48gyYikhQLmohIUpziICKSFM+giYgkxYImIpIUC5qISFIsaCIiSbGgiYgkxYIm\nIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFIsaCIiSbGgiYgkxYImIpIUC5qISFL/D+BcJhr6\nqr3jAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(c) The slope of the book is around 5/8, while the dimensional analysis is $\\frac{\\alpha^2}{\\mu\\,\\delta} = 5/8$\n",
      "\n",
      "(d) The depth of the book is around 5, while the dimensional analysis is $\\alpha/\\delta = 5$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# Figure 2: Average book shape (This take some time to run!)\n",
      "\n",
      "logging <- F # Very important for speed!\n",
      "\n",
      "alpha <- 1\n",
      "mu <- 10\n",
      "delta <- 1/6 \n",
      "initializeBook5()\n",
      "# Burn in for 100 events\n",
      "for(count in 1:100){\n",
      "  generateEvent()\n",
      "}\n",
      "numEvents <- 100000 # Average over 100,000 events\n",
      "avgBookShape <- bookShape(20)/numEvents\n",
      "for(count in 2:numEvents){\n",
      "  generateEvent()\n",
      "  avgBookShape <- avgBookShape+bookShape(20)/numEvents\n",
      "}\n",
      "\n",
      "plot(-20:20,avgBookShape,main=NA,xlab=\"Relative price\",ylab=\"# Shares\", col=\"red\", type=\"b\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAIAAADytinCAAAgAElEQVR4nO3deUAUdeMG8IdbDhFv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\nLGgiIpliQRMRydT/A/2yWtqTPK4UAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(c) The slope of the book is around 3/5, while the dimensional analysis is $\\frac{\\alpha^2}{\\mu\\,\\delta} = 3/5$\n",
      "\n",
      "(d) The depth of the book is around 6, while the dimensional analysis is $\\alpha/\\delta = 6$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# Figure 2: Average book shape (This take some time to run!)\n",
      "\n",
      "logging <- F # Very important for speed!\n",
      "\n",
      "alpha <- 1\n",
      "mu <- 10\n",
      "delta <- 1/8 \n",
      "initializeBook5()\n",
      "# Burn in for 100 events\n",
      "for(count in 1:100){\n",
      "  generateEvent()\n",
      "}\n",
      "numEvents <- 100000 # Average over 100,000 events\n",
      "avgBookShape <- bookShape(20)/numEvents\n",
      "for(count in 2:numEvents){\n",
      "  generateEvent()\n",
      "  avgBookShape <- avgBookShape+bookShape(20)/numEvents\n",
      "}\n",
      "\n",
      "plot(-20:20,avgBookShape,main=NA,xlab=\"Relative price\",ylab=\"# Shares\", col=\"red\", type=\"b\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAIAAADytinCAAAgAElEQVR4nO3dd0CU9eMH8PexN7gF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\nYII=\n"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(c) The slope of the book is around 4/5, while the dimensional analysis is $\\frac{\\alpha^2}{\\mu\\,\\delta} = 4/5$\n",
      "\n",
      "(d) The depth of the book is around 8, while the dimensional analysis is $\\alpha/\\delta = 8$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### The following code sets up the data required for Problem 4."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "download.file(url=\"http://mfe.baruch.cuny.edu/wp-content/uploads/2015/01/ziSimResults.rData_.zip\", destfile=\"ziSimResults.rData.zip\")\n",
      "unzip(zipfile=\"ziSimResults.rData.zip\")\n",
      "load(\"ziSimResults.rData\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "trying URL 'http://mfe.baruch.cuny.edu/wp-content/uploads/2015/01/ziSimResults.rData_.zip'\n",
        "Content type 'application/zip' length 130237 bytes (127 Kb)\n",
        "opened URL\n",
        "==================================================\n",
        "downloaded 127 Kb\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 4. (12 points) <font color='blue'> Score: 12/12 </font>\n",
      "\n",
      "The datafile *ziSimResults.rData* contains a list of bid and ask prices after 100 events resulting from 10,000 simulations of the SFGK model with $\\alpha = 1$, $\\mu = 10$, and $\\delta = 1/5$. The $j$th element of the list has results for an initial book configuration with $q_b = j$ shares on the bid side and $q_a = 1$ share on the ask side."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%R head(data.frame(ziSimResults))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "array([[-1., -1., -2.,  0., -2., -2.],\n",
        "       [ 2.,  4., -1.,  3.,  2.,  0.],\n",
        "       [-2., -3., -1., -2.,  0., -4.],\n",
        "       [ 2., -1.,  0.,  3.,  4.,  1.],\n",
        "       [-2., -2., -1., -2.,  0., -1.],\n",
        "       [ 4.,  3.,  0.,  3.,  3.,  1.],\n",
        "       [-1.,  1., -1., -2.,  3., -3.],\n",
        "       [ 3.,  3.,  3.,  1.,  5.,  2.],\n",
        "       [-1., -2., -2.,  0., -2., -1.],\n",
        "       [ 3.,  1.,  2.,  3.,  2.,  3.],\n",
        "       [-1., -1., -1., -1.,  0.,  1.],\n",
        "       [ 2.,  0.,  2.,  2.,  3.,  3.],\n",
        "       [-1., -1.,  2., -1., -1., -1.],\n",
        "       [ 2.,  3.,  3.,  1.,  2.,  1.],\n",
        "       [ 0.,  0., -1., -1., -1.,  1.],\n",
        "       [ 3.,  4.,  1.,  2.,  2.,  2.],\n",
        "       [-1., -1., -1., -1., -1.,  3.],\n",
        "       [ 2.,  1.,  1.,  0.,  2.,  4.],\n",
        "       [-1.,  1., -1., -1.,  1.,  2.],\n",
        "       [ 0.,  2.,  0.,  3.,  3.,  3.]])"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(a) For each size $q_b$ at best bid, compute the mean mid-price after 10,000 events and with error computed as standard deviation of the mean.\n",
      "\n",
      "(b) Plot mean mid-price vs size at best bid, reproducing Figure 3 of the lecture slides. \n",
      "Remember to include error bars!\n",
      "\n",
      "(c) Repeat part (b) with the order book imbalance $I$ on the x-axis, reproducing Figure 7 in the lecture slides.\n",
      "\n",
      "(d) If you see an order book with large quantity at the bid and small quantity at the offer, what does it tell you about the future price?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R    # (a)\n",
      "\n",
      "# Parse the original data into a data frame\n",
      "bidAskPrice <- data.frame(ziSimResults)\n",
      "\n",
      "# Declare a mid price matrix which is used to store the mid price\n",
      "midPrice <- matrix(nrow = 10000, ncol = 10)\n",
      "\n",
      "# Calculate the mid price matrix\n",
      "for(k in 1:10){\n",
      "    for(j in 1:10000){\n",
      "        midPrice[j, k] = (bidAskPrice[j, 2*k-1] + bidAskPrice[j, 2*k])/2\n",
      "    }\n",
      "}\n",
      "\n",
      "meanVec = vector(10, mode = \"numeric\")\n",
      "sdVec = vector(10, mode = \"numeric\")\n",
      "\n",
      "# Calculate the mean and standard deviation of the mean\n",
      "for(i in 1:10){\n",
      "    meanVec[i] = mean(midPrice[,i])\n",
      "    sdVec[i] = sd(midPrice[,i])/sqrt(10000)\n",
      "}\n",
      "\n",
      "cat(\"The mean mid price after 10000 event is: \", meanVec, \"\\n\")\n",
      "cat(\"The standard deviation of the mean is: \", sdVec, \"\\n\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "The mean mid price after 10000 event is:  0.0059 0.2155 0.4135 0.56635 0.6685 0.7411 0.8053 0.80955 0.8388 0.83435 \n",
        "The standard deviation of the mean is:  0.01537986 0.0143163 0.01310835 0.01229115 0.01123358 0.01038017 0.01019091 0.009888385 0.009779878 0.009617315 \n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R    # (b)\n",
      "\n",
      "# size of best bid\n",
      "q_b <- 1:10\n",
      "\n",
      "# Start to plot and add the error bars\n",
      "plot(q_b,meanVec,xlab=\"Size at best bid q_b\",ylab=\"Mean mid price\",main=\"Mean mid price after 100 events vs size at best bid q_b\", col=\"red\")\n",
      "q_bHigh <- q_b\n",
      "meanHigh <- meanVec + sdVec/2\n",
      "q_bLow <- q_b\n",
      "meanLow <- meanVec - sdVec/2\n",
      "arrows(q_bLow, meanLow, q_bHigh, meanHigh, length=0.1, angle=90, code=3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAYAAAB91L6VAAAEJGlDQ1BJQ0MgUHJvZmlsZQAAOBGF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\nQIAAzDGAAAIIIIBAEgT+D8MDRMCrdXaNAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R    # (c)\n",
      "\n",
      "# Imbalance\n",
      "I <- (q_b-1)/(q_b+1)\n",
      "\n",
      "# Start to plot and add the error bars\n",
      "plot(I,meanVec,xlab=\"Imbalance(I)\",ylab=\"Mean mid price\",main=\"Mean mid price vs Imbalance\", col=\"red\", type=\"b\")\n",
      "IHigh <- I\n",
      "meanHigh <- meanVec + sdVec/2\n",
      "ILow <- I\n",
      "meanLow <- meanVec - sdVec/2\n",
      "arrows(ILow, meanLow, IHigh, meanHigh, length=0.1, angle=90, code=3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAYAAAB91L6VAAAEJGlDQ1BJQ0MgUHJvZmlsZQAAOBGF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\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(d) If an order book has large quantity at the bid and small quantity at the offer, imbalance increases, accrording to graphs above, the future price increases."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Is the market price a martingale?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 5. (4 points)  <font color='blue'> Score: 2/4 </font>\n",
      "\n",
      "A derivatives quant explains (patiently) to you that asset prices are martingales (informally speaking that expected price changes are zero). Do you agree? How is your understanding consistent with the derivative quant\u2019s understanding?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Answer:\n",
      "\n",
      "The fundamental pricing theorem says that the market is arbitrage free only if there exists a risk neutral probability such that the discounted price process is a martingale. This theorem has two conditions: under the risk neutral measure and the discounted price process, not the real price process. So, normally, the price of the asset under the real world probability is not a martingale."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<font color=blue> (2pts off) The key points are:\n",
      "* Microstructure models show that if you condition on the state of the book or the history of order flow, you can predict future prices. \n",
      "\n",
      "* If you don\u2019t condition either on the state of the order book or on the history of order flow (as might be typically the case for delta hedgers), the price process can be a martingale."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}